Performance analysis of max-min path selection scheme in multi-hop DF cooperative system over Nakagami-m channels

In this paper, we find cumulative distribution function and probability density function (PDF) of max-min Gamma random variable (RV) in terms of converging power series. By using the PDF of this RV, the average bit error rate of max-min criterion based path selection in multi-hop decode-and-forward (DF) cooperative communication over Nakagami-m fading channels is analyzed. Coding gain and diversity order of the max-min criterion based path selection scheme are analytically obtained. It is inferred by the analysis and simulation that the max-min path selection provides significant performance gain in multi-hop DF cooperative system; moreover, the diversity of the considered system is independent of the number of hops.